What Was Rational Expectations? Bueller?

When I wrote that rational expectations was a theory Y, a commenter asked me to explain rational expectations. I will do so below the fold.

1. Start with a theory of business cycles that says that employment is driven by the relationship between labor productivity and real wages. In particular, when real wages are high relative to productivity, you get a lot of unemployment.

2. Next, think of workers as setting wage demands on the basis of expected inflation. If workers expect prices to rise at 3 percent per year, then they will look for wages increases of 3 percent plus the rate of increase in productivity.

Together (1) and (2) provide a model of employment as determined by the forecast error in prices. If workers are surprised by high inflation, they will set real wages at a low level, and there will be a lot of labor demand, and hence very little unemployment. If they are surprised by low inflation, there will be low labor demand, and hence a lot of unemployment.

This in turn suggests that expansions in aggregate demand are effective at increasing output if and only if they cause upside surprises in inflation. For example, assume that workers base their expectations of inflation on recent past inflation. One popular model is "adaptive expectations," in which your expectations of inflation in period t are a weighted average of the expectations you had in period t-1 and the actual outcome for inflation in period t-1. Then a big increase in the money supply in period t will cause more inflation than expected, which will reduce real wages, increase labor demand,, and increase employment.

3. So far, we have workers making systematic errors in forecasting prices. The Fed can always surprise them by speeding up the money-printing process and causing more inflation than expected. What if workers, instead of naively looking backward, start to anticipate Fed behavior? In that case, known as rational expectations, workers will not commit systematic forecasting errors. They can be surprised, but they cannot be fooled. Surprises consist of events that surprise the monetary authority as much as they surprise workers. Being fooled means being surprised by the monetary authority, and that does not happen. In that case, discretionary monetary policy is ineffective.

What made rational expectations fun was the math. You use something called stochastic differential equations to solve rational expectations models. Because these equations are more complex than the ordinary calculus that used to be standard in economics, you can feel superior.

The typical macro model of the past thirty years combines rational expectations with some arbitrary friction in price adjustment (most infamously, the cost of printing new menus). The friction gives rise to unemployment, and the rational expectations assumption makes the math complicated and cool. Naturally, the implication of the model is that the economy works best when everyone's price expectations are satisfied, which means that the Fed should do inflation targeting.

4. What's wrong with rational expectations? For me, the problem is that I have never bought (1)-(2) as an explanation for unemployment. In graduate school, what I preferred was "general disequilibrium theory." If one market gets out of whack, then other markets get out of whack. The challenge was to explain how markets get out of whack. I thought in terms of sticky prices.

In the past couple of years, I have been questioning the whole idea of looking for out-of-line prices as an explanation for recessions. I have discarded the mental model of the economy as a set of Walrasian equations in need of a solution vector of prices. Instead, I have a mental model of people trying to identify comparative advantage so that they can specialize and trade. Our production process is so abstract and roundabout that this is very difficult to do. Entrepreneurs attempt all sorts of businesses, many of which fail.

If yesterday's pattern of specialization and trade continues to work reasonably well today, then employment remains high. However, if yesterday's pattern is no longer sustainable, then the economy must undergo a recalculation.

I have never believed in modeling the business cycle as determined by expectation errors in forecasting overall inflation. Hence, I never thought that it mattered so much whether inflation forecasts were rational or not. Hence, I never thought that rational expectations macro modeling was an avenue worth pursuing.

The academic market made a different decision. In fact, I would argue that the market emerged from in-breeding of fewer than a dozen economists in the late 1970's. Folks like Dornbusch and Fischer at MIT, Lucas at Chicago, Sargent and Wallace at Minnesota. The in-breeding created a line of deformed, intellectually stunted macroeconomists. They could think in terms of Euler equations, but they could not begin to understand an actual economy.

Comments and Sharing

"They could think in terms of Euler equations, but they could not begin to understand an actual economy."

It is not just the past, it is still happening today.... you have accurately described my recent 1-year experience in a PhD program. It was all about math, and had nothing to do with learning how an actual economy acutally works.

I also don't buy (1)-(2), but I hardly think that this is a reason to get rid of rational expectations. Quoting Cowen,

"Whenever we wish to specify a coordination problem, rational expectations theory requires us to justify, or at least outline, the underlying informational asymmetries. I view the rational expectations assumptions as a useful form of discipline. Rational expectations does not rule out significant marketplace errors, but it does require us to specify the source of these errors in some explicit informational asymmetry."

I think this "discipline" view of RE is exactly right, even if RE is not a useful descriptive assumption about the real world, and even if (here I agree with you) it was used in conjunction with really crappy models about the labor market.

Your initial model is not presented with maximum plausibility. Why focus on workers' forecast of inflation, and their corresponding wage "demands," without mentioning employers' forecasts of inflation, and their corresponding wage offers? And the presentation should make it clear that it is inflation expectations, rather than actual inflation, that determine these wage demands/offers. If workers and employers (supposing we can treat these groups as undifferentiated aggregates) agree in their forecasts of inflation, there will be normal employment/unemployment. If workers expect more inflation than employers do, there will be extra unemployment; if workers expect less inflation than employers, there will be less-than-normal unemployment. (This conflict in expectations will also affect wage rates.) The important factor is not an error in the workers' forecast of inflation but rather a divergence between their forecast and that of the employers.

True, actual inflation might be relevant in a secondary way--for example, if we "assume that workers base their expectations of inflation on recent past inflation." But even then, there will be an effect on employment only if employers form their expectations *differently*.

"This in turn suggests that expansions in aggregate demand are effective at increasing output if and only if they cause upside surprises in inflation." This should read: ". . . only if they cause employers to expect higher inflation than workers expect."

It seems to me that a divergence in inflation expectations between workers and employers would, indeed, have an effect on (un)employment. But I would expect such divergences to be extremely rare, and so to explain few, perhaps no, real-world episodes of exceptionally high (or low) unemployment.

On the other hand, "recalculation" is taking place all the time; that makes it a poor explanation for brief periods of exceptional unemployment.

@Jacob Oost: (Ordinary) differential equations are a basic math course, but stochastic or partial differential equations are not. ( double-checked with my physicist friend.) It is the latter that have become popular in RE and finance modelling.

Oh. Well, it's a course in ODE and PDE, and it's what I have to take before the "real" classes later on. I don't know if it covers stochastic, let me check..........nope, sure doesn't. I assume it'll be covered later in actual physics classes as needed.

With 15 trillion or so in debt, the major industry today in the US is harvesting future disposable income. Seining for the big fish. Knowing the time stream of future income only requires the ability to predict the weather, hurricane hits on refineries, war, pestilence, and the trifles that await in the House of Saud. It doesn't really matter if you get it right, just as long as you hit the middle of the expectation.

If market for future income gets "out of whack", all others must adjust. So there is no real problem. Just assume omniscience or smooth and knowable PDF,s and RE is fine.

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